用 LaTeX 记录的数理课笔记。对于期末复习有所帮助。
为方便阅读(母语 + 字母符号在汉字中更易区分),语言采用为中文。
使用 UTF-8
编码。
已收录本人的(排名并不按照学期顺序):
- 微积分A (2) Calculus 2
- 概率论与数理统计 Probability and Statistics
- 数学物理方法 Methods of Mathematics and Physics
- 量子力学 Quantum Mechanics
- 统计力学 Statistical Mechanics
- 电动力学 Electrodynamics
- 核辐射物理及探测学 Nuclear Radiation Physics and Detection
hair.tex
预设定了统一的笔记格式,在 \input{hair.tex}
之前,你还需要定义一些笔记性质相关的变量。
\def\coursename{数理方程}
% default: 笔记
\def\coursefullname{数理方程与特殊函数}
% default: \coursename
\def\courseEnglishname{Mathematical Equations and Special Functions}
% default: Note
\def\titleannotation{基于姚国武老师讲义整理}
% default no notation
\def\authorname{Dait}
% default: Dait
\def\authorEnglishname{Dait}
% default: Dait
\def\departmentname{THU}
% default: THU
\def\emailaddress{[email protected]}
% default: [email protected]
\def\beginday{2022/2/24}
% default: 2021
\def\endday{2022/5/20}
% default: \number\year/\number\month/\number\day
% \date{\beginday~-~\endday}
% if same as \beginday, \dait{\beginday} only
\input{../hair.tex}
\input{../head.tex}
% options
\showemail
% default hide email
\contentfalse
% default show content
\parskiptrue
% default no extra parskip
\begin{document}
\firstandforemost
\section{偏微分方程的定解问题}
% mainbody starts here...
\end{document}
head.tex
中定义了一些定义帮助简化输入。
\int\iti\e{-x^2}\d x=\sqrt\pi.
% \iti = -infty to +infty
% \e = e^
% \d = d
vs.
\int_{-\infty}^{+\infty}\mathrm e^{-x^2}\,\mathrm dx=\sqrt\pi.
\dd[n-1]x\dv yx = \dv[n]yx.
% \dd x = d/dx
% \dv yx = dy/dx, derivative
vs.
\frac{\mathrm d^{n-1}}{\mathrm dx^{n-1}}\frac{\mathrm dy}{\mathrm dx}=\frac{\mathrm d^ny}{\mathrm dx^n}.
\pv yx, \pv[n]yx, \pw zxy.
% \pv yx = ∂y/∂x, partial derivative
% \pw zxy = ∂^2z/∂x∂y, w = double v
vs.
\frac{\partial y}{\partial x}, \frac{\partial^n y}{\partial x^n}, \frac{\partial^2 z}{\partial x\partial y}.
example 4:
\ave A=\bra\psi A\ket\psi=\int\bra\psi A\ket x\bs3\brkt x\psi\d x.
% \bra x = <x|
% \ket x = |x>
% \brkt x\psi = <x|ψ>
% \bs3 = backspace 3 pt
vs.
\left\langle A\right\rangle=\left\langle\psi\right\vert A\left\vert\psi\right\rangle=\int\left\langle\psi\right\vert A\left\vert x\right\rangle\hspace{-3pt}\left\langle x\middle\vert\psi\right\rangle\,\mathrm dx.
About space
\qquad % 2em
\quad % 1em
\enspace % 0.5em
\; % 5/18em
\: % 4/18em
\, % 3/18em
\! % -3/18em